Pipe Flow Calculations - Clarkson University

values recommended for commercial pipes given in a textbook on Fluid Mechanics by F.M.
White is provided at the end of these notes.
Colebrook Equation
1 ⎡ε
/ D 1.26
=− 4.0 log10
⎢ +
f
⎣⎢
3.7 Re f
⎤
⎥
⎦⎥
Zigrang-Sylvester Equation
1 ⎡ε
/ D 5.02 ⎛ε
/ D 13 ⎞⎤
=−4.0 log10 ⎢ − log10
⎜ + ⎟
f
3.7 Re 3.7 Re
⎥
⎣
⎝ ⎠⎦
Non-Circular Conduits
Not all flow conduits are circular pipes. An example of a non-circular cross-section in heat
exchanger applications is an annulus, which is the region between two circular pipes. Another is
a rectangular duct, used in HVAC (Heating, Ventilation, and Air-Conditioning) applications.
Less common are ducts of triangular or elliptical cross-sections, but they are used on occasion.
In all these cases, when the flow is turbulent, we use the same friction factor correlations that are
used for circular pipes, substituting an equivalent diameter for the pipe diameter. The equivalent
diameter D , which is set equal to four times the “Hydraulic Radius,” R is defined as follows.
e
h
D
e
Cross -Sectional Area
= 4Rh
= 4×
Wetted Perimeter
In this definition, the term “wetted perimeter” is used to designate the perimeter of the crosssection
that is in contact with the flowing fluid. This applies to a liquid that occupies part of a
conduit, as in sewer lines carrying waste-water, or a creek or river. If a gas flows through a
conduit, the entire perimeter is “wetted.”
Using the above definition, we arrive at the following results for the equivalent diameter for two
common cross-sections. We assume that the entire perimeter is “wetted.”
Rectangular Duct
b
a
For the duct shown in the sketch, the cross-sectional area is ab , while the perimeter is 2( a+
b)
so that the equivalent diameter is written as follows.
2